Modelling correlated clinical outcomes in health technology appraisal

Many clinical treatments have multiple effects that can only be effectively captured on multiple outcome scales. It might be important to understand how these outcomes are correlated to evaluate the effectiveness and cost-effectiveness of treatments in decision models.

The probabilities are estimated that both, one, or neither outcome occurs, given estimates of the marginal probability for each outcome and information about the correlation between them. Methods are shown for different measures of association. Lower and upper bounds for the correlation coefficient are calculated for given values of the marginal probabilities. The approach is illustrated using a simplified decision model based on a recent evaluation of adalimumab, a biologic drug for psoriatic arthritis.

Assuming the outcomes are positively correlated, the probability of both a skin and arthritis response after adalimumab was estimated to be 0.387 (95% confidence interval 0.210-0.570). The incremental cost-effectiveness ratio (ICER) of adalimumab versus no biologic is £18,500 per quality-adjusted life-year (QALY). The ICER increases to £19,500 per QALY if the responses are independent.

Estimates of ICERs can be sensitive to assumptions about how multiple outcomes are correlated. These assumptions should be explored in univariate and probabilistic sensitivity analyses.